Simplify the following expression: $x = \dfrac{1}{5r} - \dfrac{1}{9r}$
Solution: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $5r$ and $9r$ $\lcm(5r, 9r) = 45r$ $ x = \dfrac{9}{9} \cdot \dfrac{1}{5r} - \dfrac{5}{5} \cdot \dfrac{1}{9r} $ $x = \dfrac{9}{45r} - \dfrac{5}{45r}$ $x = \dfrac{9 -5}{45r}$ $x = \dfrac{4}{45r}$